In order to hold to the lowest possible level the force necessary for the elevation or lowering of a rear seat headrest, whether this be done manually or by remotely actuated, automatic means, it is of advantage if the holding bars of said head rest move within a guide component wherein a radial clearance is present. Counter to this concept, the danger is present, that where such play exists between a holding bar and its support, that the headrest will wobble during driving periods and emit rattling noises. A secure retention of the headrest in the reclining seat back requires, further, auxiliary aids such as springs or motor powered drives, in order to be able to remotely allow the headrest to move into its lowest position. In a backseat arrangement made known by DE 195 32 260 C2, the holding bar of a headrest is held by force in its lowest position of elevation by means of a compression spring acting in that direction. The spring becomes active, if an arresting means, in the form of a spring projection obstructingly resting within a notch in the holder rod is removed therefrom by remote action. The problem which arises is that a wobble-free seating of the headrest is dependent upon friction, whereby high adjusting forces become necessary. From this situation, a large adjustment force of the spring is required, which in turn demands a spring of correspondingly large dimensions. This disadvantage brings in turn, the problem that the user, upon the lifting of the headrest by hand, must overcome not only the frictional resistance between the holding bar and the support, but also force of the spring, which exercises this force in a downward direction. Yet another problem in the described arrangement, and also in the case of a motor powered lowering, is that the active connection between the spring or the drive must finally be dismantled, when the headrest is to be removed from the reclining seat back.